Rheological Phenomena in Focus

159 Pages·1993·22.071 MB·1-156\159

by  D.V. Boger and K. Walters (Eds.)

RHEOLOGY SERIES
Advisory Editor: K. Walters FRS, Professor of Applied Mathematics, University of Wales, Aberystwyth, U.K.
Vol. 1 Numerical Simulation of Non-Newtonian Flow (M.J. Crochet, A.R. Davies
and K. Walters)
Vol. 2 Rheology of Materials and Engineering Structures (Z. Sobotka)
Vol. 3 An Introduction to Rheology (H.A. Barnes, J.F. Hutton and K. Walters)
Vol. 4 Rheological Phenomena in Focus (D.V. Boger and K. Walters)
The photograph used on the front cover shows the secondary flow induced when a sphere is rotated in a
beaker of elastic liquid (a 1.5% aqueous solution of polyacrylamide). The density of the dye used to make
the streamlines visible is greater than that of the polymer solution and this is the reason for the lack of any
symmetry about the equatorial plane. The photograph used on the backcover is described on page 111.
R h e o l o g i c al
P h e n o m e na
in F o c us
D.V. Boger
Professor of Chemical Engineering
University of Melbourne
Parkville, Australia
K. Walters FRS
Professor of Applied Mathematics
University of Wales
Aberystwyth, UK
1993
Elsevier
Amsterdam - London - New York - Tokyo
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To
Lie and Mary
PREFACE
On the book shelf of most practioners in the field of (Newtonian) Fluid Mechanics
will be a copy of Van Dyke's classical compilation of photographs in "An Album of Fluid
Motion" published in 1982 by The Parabolic Press, Stanford, California. Often, the
Album is in every sense a desk copy and, for those of us who teach Fluid Mechanics, it
is an indispensible teaching aid. The opening sentiments in Van Dyke's book run thus:
"We who work in fluid mechanics are fortunate, as are colleagues in a few other fields
such as optics, that our subject is easily visualized". Who can argue with such a
statement? But equally true is that those of us who work in /ion-Newtonian Fluid
Mechanics are even more fortunate and we often talk in general terms of "unusual and
bizarre phenomena not encountered in classical Fluid Mechanics". Many of these
phenomena are very photogenic and they provide a useful backdrop to introduce the
rather difficult subject called Rheology. Hence the motivation for "Rheological Pheno
mena in Focus".
The idea was greeted with enthusiasm by our many colleagues and friends in the
field and we very much hope that those who teach Rheology or have to convince
colleagues of the relevance of the subject in an industrial setting will find the book as
useful as Van Dyke's Album has become in Newtonian Fluid Mechanics.
The selection of photographs cannot be considered to be complete and we freely
admit that our choice has been dictated as much by the quality of the available
photographs as by scientific considerations. The alternative would have led to a book
containing photographs of very variable quality and, even then, there would have been
no guarantee of completeness without embarking ourselves on an extensive pro
gramme of flow visualization.
We have not felt it necessary to include a complete historical survey of the various
phenomena or to provide a deep discussion of the underlying physics. These are
already adequately covered in the many excellent text books in the field. Rather, we
view the present text as a 'support manual'.
As a general rule, we refer to rheological terms without seeing the need to define
them. We take it for granted that most readers will either have a working knowledge
of such terms or will have easy access to one of the many textbooks on the subject. A
simple Glossary is given at the end of the book for the casual reader.
We wish to thank those who have so readily allowed us access to their published
(and unpublished) photographs. D.V. Boger would like to acknowledge the invaluable
assistance of Mr. Rod Binnington and Mrs. Christine Collis. A special thank you goes
to Mr. Robin Evans who has been responsible for the final art and photographic work
and to Mrs. Pat Evans who typed the final manuscript with her usual patience and
excellence.
David Boger and Ken Walters
vii
CHAPTER 1
INTRODUCTION
1.1 What is Rheology?
Rheology is defined as the Science of Deformation and Flow. This definition would
allow a study of all materials which are capable of deformation, but Hookean elastic
solids and Newtonian viscous fluids are invariably considered to be outside the scope
of Rheology and the emphasis is therefore on materials between these classical
extremes. The term Viscoelastic' is used to describe the behaviour of such materials.
The present book is basically concerned with flow phenomena and must therefore
involve a consideration of fluids. If, as indicated, we omit any consideration of New
tonian fluids, we are by implication restricted to the so called non-Newtonian fluids.
Furthermore, since gases are of no concern to us, we shall refer generally to non-New
tonian liquids. Such liquids may or may not possess strong elastic properties. If they
do, they are now generally called 'elastic liquids'.
Although non-Newtonian inelastic liquids exhibiting shear thinning or shear thick
ening behaviour constitute an important group of industrial materials, they are not
our primary concern in the present book, since most of the extravagant rheological
phenomena are exhibited by strongly elastic liquids. In general terms, therefore, the
present book is predominantly concerned with viscoelastic effects in flow.
One material which has often been used in flow visualization experiments is a
constant-viscosity elastic liquid, the so-called 'Boger fluid' (see, for example, D.V.
Boger, J. Non-Newtonian Fluid Mechanics, 3,1977/78,87). This material is convenient
in flow visualization experiments because it allows viscoelastic phenomena to be
identified in flow fields in the absence of variable-viscosity effects.
1.2 Why Flow Visualization?
Flow visualization has always been important in the study of fluid mechanics, not
only to visualize and record the flow, but also in the development of the analytical and
numerical tools required to solve flow problems. The former use should not be under
estimated, since many of the extravagant effects of viscoelasticity are very photogenic
and the many available flow visualization pictures have enriched the field of non-New
tonian Fluid Mechanics.
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A Fig. 1.1. Low Reynolds number (creeping) re-entrant tube flow in a 12 to 1 contraction. The
small tube protrudes up into the larger tube 41.3% of the upstream tube diameter. Shown
on the left of the frame are the observed streamlines for an inelastic Newtonian liquid in
comparison with the numerical prediction (right-hand frame) generated with a commercial
software package.
(From D.V. Boger and R.J. Binnington, J. Non-Newtonian Fluid Mechanics, 35, 1990, 339.)
2
The second motivation for flow visualization is less artistic and more scientific. It
has a part to play in the pursuance of the Scientific Method in non-Newtonian Fluid
Mechanics. The behaviour of liquids is first characterized by means of constitutive
equations relating suitable stress and deformation variables. These are then solved, in
conjunction with the conservation equations for mass and linear momentum, to predict
behaviour in complex flows. The final sequence involves the comparison of the result
ing theoretical predictions with experimental observations, which are often given in
the form of flow-visualization pictures.
In the case of Newtonian Fluid Mechanics the application of the Scientific Method
is routine, since, in this case, the governing equations reduce unambiguously to the
well known Navier-Stokes equations. Figures 1.1 and 1.2 give two representative
examples of the success of the Scientific Method for a Newtonian liquid. Figure 1.1
concerns flow into a re-entrant tube from a larger tube upstream; the left hand side of
A Fig. 1.2. Flow induced by an immiscible Newtonian liquid drop falling in another Newtonian
liquid in the Hadamard-Rybczynski regime — comparison between flow visualization and
numerical prediction.
(From M. Coutanceau, R. Bouard, M. Hellou, A. Maalouf and A. Texier, Flow Visualization
IV, Proceedings of the Fourth International Symposium on Flow Visualization, Ed. Claude
Veret, Ecole Nationale Superieure de Techniques Avancees, Paris, 1986, 401.)
3
the image illustrates the streamlines observed in the flow field, whilst the right hand
side shows the numerically-calculated streamlines. Similarly, Fig. 1.2 illustrates the
streamlines for a glycerine drop falling axially in a vertical tube, with a comparison
again shown between observation and numerical prediction. Nowadays, no one would
be surprised by such excellent agreement between theory and observation for a
Newtonian liquid.
The situation is more fascinating in non-Newtonian Fluid Mechanics. In this case,
there are many possible constitutive equations available for different classes of mate
rial behaviour. Thus the equivalent set of equations to the Navier-Stokes equations is
uncertain. This is particularly true for elastic liquids. Flow visualization is therefore
of extreme importance in non-Newtonian Fluid Mechanics, where a great deal of effort
is being expended in developing the appropriate tools to solve flow problems of
fundamental and practical interest.
1.3 On Flow-Visualization Techniques
Non-Newtonian liquids are generally quite viscous and are usually encountered in
laminar, and many times, creeping flows. The flow visualization techniques required
for such flows are not complicated and there has not been a fundamental change in the
technology for flow visualization in the last century. The upper frame of Fig. 1.3 is a
reproduction of a photograph for laminar flow of a Newtonian liquid through an abrupt
circular contraction where dyed fluid elements were used to mark the flow lines. This
photograph was published with many others in a paper by H.S. Hele Shaw in 1898
(Trans. Instn. Naval Archit. 40,1898, 21). Contrasted with the Hele Shaw observation
is a 1988 picture (Fig. 1.3b) obtained with an apparatus similar to that illustrated in
Fig. 1.4. The photographic image shown in Fig. 1.3b was obtained with a low power
laser light source used with a cylindrical lens to generate a planar light source. For
good quality production, the image was recorded on photographic film, although many
investigators have now moved to video recorders. Multiple image techniques are not
appropriate in some flows, where an exposure time of minutes may be required to
delineate the flow field. Highly reflecting tracer particles suspended in the fluid enable
photographic images of the trajectory to be recorded. It is important that these
reflecting particles do not settle in the flow field and thus judicious choice is required
in selecting appropriate tracer particles.
Fig. 1.3 (opposite). Laminar low-Reynolds-number flow of a Newtonian fluid in a tubular ^
entry — then, 1898 (a) and now, 1988 (b). (a) Dyed fluid elements were used to mark the flow
lines. (From H.S. Hele-Shaw, Trans. Instn. Naval Archit. 40,1898,21.) (b) Reflecting coated
mica particles used as tracer particles. (Photograph courtesy of R.J. Binnington, The University
of Melbourne, 1988.)
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(a)
(b)